Question: I need you to solve these question please 3. Exercise 3: Persons entering a blood bank are such that 1 in 3 have type Of

I need you to solve these question please

I need you to solve these question please 3. Exercise 3: Persons

3. Exercise 3: Persons entering a blood bank are such that 1 in 3 have type Of blood and 1 in 15 have type O- blood. Consider three randomly selected donors for the blood bank. Let X denote the number of donors with type O+ blood and Y denote the number with type O- blood. (a) Find the probability distributions for X and Y and represent them graphically. (b) Find the Cumulative Distribution Function (CDF) of X and Y and plot them. (c) Are X and Y independent random variables? (d) Find the probability distribution of Z := X + Y the number of donors who have type ( blood. (e) Calculate uz := E(Z) and oz := V(Z). Course code: STAT 211 Assignment 2 - Page 2 of 2 Due Date: 4/10/2020 (f) Find the mgf of Z and deduce the value of E(Z3). (g) Find the probability that Z is between pz + 20z

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